Simplify; express your answer in exponential form. Assume $n\neq 0, p\neq 0$. $\dfrac{{(n^{-4})^{3}}}{{(np^{-4})^{5}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${n^{-4}}$ to the exponent ${3}$ . Now ${-4 \times 3 = -12}$ , so ${(n^{-4})^{3} = n^{-12}}$ In the denominator, we can use the distributive property of exponents. ${(np^{-4})^{5} = (n)^{5}(p^{-4})^{5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(n^{-4})^{3}}}{{(np^{-4})^{5}}} = \dfrac{{n^{-12}}}{{n^{5}p^{-20}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{-12}}}{{n^{5}p^{-20}}} = \dfrac{{n^{-12}}}{{n^{5}}} \cdot \dfrac{{1}}{{p^{-20}}} = n^{{-12} - {5}} \cdot p^{- {(-20)}} = n^{-17}p^{20}$.